Amplification of longitudinal stress pulses in elastic bars with an intermediate tapered region

Abstract

Experiments are performed to study the amplification of longitudinal pulses which propagate along tapered elastic bars in the direction of decreasing cross-sectional area. Each bar specimen is composed of two uniform cylindrical end sections of different radius joined by a tapered transition in the form of a cone frustrum. The amplification of a pulse which propagates from the large end to the small end in such a bar is shown to depend on the spatial pulse length (nondimensionalized with respect to the length of the transition region) for a given ratio of the terminating cross-sectional areas. The observed amplification is plotted over a wide range of nondimensionalized pulse lengths for several choices of the overall area ratio. For very short and very long pulses, the amplification approaches the limiting values given by simple equations which involve only the geometric parameters of the bar. The factors which influence the amplitude and shape of pulses which are reflected from the cone frustrum are discussed briefly.